What is the first term of the sequence? What is the common ratio between terms? Use these values in the explicit equation for geometric sequences.
Equation: a_n=7640(0.1)^(n-1) Value of a_6: 0.0764
Practice makes perfect
Equations for geometric sequences follow a specific format.
a_n= a_1( r)^(n-1)
In this form, a_1 is the first term, r is the common ratio from one term to the next, and a_n is the {\color{#FF0000}{n}}^\text{th} term in the sequence. For this exercise, the first term is a_1= 7640. To find the common ratio r we can find the quotient between any two consecutive terms. For simplicity, let's use the first two terms.
a_2/a_1=764/7640= 0.1
The common ratio of the geometric sequence is 0.1.
7640* 0.1 ⟶764* 0.1 ⟶76.4* 0.1 ⟶7.64...
By substituting these two values into the explicit equation and simplifying, we can find the formula for this sequence.
This equation can be used to find any term in the given sequence. To find a_6, the {\color{#FF0000}{6}}^\text{th} term in the sequence, we substitute 6 for n.
